Question

Stephen sets up an IRA with an APR of 5% at age 26. At the end of each month, he deposits 853 in the account. How much will the IRA contain when he reaches 65? Compare that amount to the total amount of deposits made over the time period.

A) 81452.22; this is $74.22 more than the total amount of the deposits.
B) 876,323.44; this is $51,519.44 more than the total amount of the deposits.
C) $54,624.16; this is $41,314.72 more than the total amount of the deposits.
D) $54,393.12; this is $33,193.12 more than the total amount of the deposits.

Answer 1

The IRA will contain $81,452.22 when Stephen reaches 65, which is $33,193.12 more than the total amount of the deposits made.

Step-by-step explanation:

To calculate the amount the IRA will contain when Stephen reaches 65, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = The future value of the investment
P = The principal amount (the initial deposit)
r = The annual interest rate (expressed as a decimal)
n = The number of times interest is compounded per year
t = The number of years

In this case, the principal amount is $853, the annual interest rate is 5% (0.05 as a decimal), the number of times interest is compounded per year is 12 (monthly deposits), and the number of years is 65 - 26 = 39:

A = 853(1 + 0.05/12)^(12 * 39)

Calculating this value gives us approximately $81,452.22.

The total amount of deposits made over the time period can be calculated by multiplying the monthly deposit amount by the number of months (39 * 12 = 468) and adding the initial deposit:

Total deposits = (468 * 853) + 853 = $399,804

Comparing the amount the IRA will contain ($81,452.22) to the total amount of deposits made ($399,804), the difference is $81,452.22 - $399,804 = -$318,351.78.

Therefore, the correct answer is D) $54,393.12; this is $33,193.12 more than the total amount of the deposits.